The line of sight distance for two antennas of height 100 m and 400 m above earth surface is approximately: (Given \( R = 6400 \text{ km}, \sqrt{20} = 4.5 \))

A galvanometer of resistance \(76 \Omega\) gives full scale deflection when only \(5 \%\) of total current passes through it. The value of shunt is :

The radius of the first orbit in Bohr's hydrogen atom is 0.53\(\text{\AA}\). The radius of fourth orbit of this atom will be:

A charge of 50 \( \mu C \) is uniformly distributed on the surface of a thin spherical shell of radius 10 cm. The electric field at a point at a distance of 5 cm from the center of the shell is

In a meter bridge, the null point is found at a distance of 60 cm from end A. If a \( 5 \text{ } \Omega \) resistor is now connected in series with S, the null point occurs at 50 cm. The values of R and S are, respectively

In the context of the Photoelectric effect, identify the statements which support quantum nature of light.
(A) The electric charge of photoelectrons is quantized
(B) The maximum kinetic energy of photoelectrons depends on the frequency of the incident light, but is independent of its intensity
(C) The photoelectric emission is an instantaneous process without any apparent time lag, even when the incident radiation is made exceedingly dim
(D) There is a minimum frequency of light below which no photoelectrons are emitted
Choose the correct answer from the options given below:

Two slits are made 0.8 mm apart and the screen is placed 1.5 m away. What should be the width of each slit to obtain 8 maxima of the double slit pattern within the central maximum of the single slit pattern?

For the given 5 values \(24,18,33,42,24\); the \(3\) -year moving averages are:

Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
Benzoic acid in the presence of conc. \(HNO _3\) and conc. \(H _2 SO _4\) gives major product as:

It is known that \(3\%\) of plastic bags manufactured in a factory are defective. Using the Poisson distribution on a sample of 100 bags, the probability of at most one defective bag is :

The value of the determinant \(\left|\begin{array}{cc}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|\) is:

Consider the equation of the line \(\vec{r}=-\hat{i}+2 \hat{k}+\mu(4 \hat{i}-\hat{j}+2 \hat{k})\).
Match List-I with List-II

List-I	List-II
(A) It passes through the point	(I) \(4,-1,2\)
(B) Its direction ratios are	(II) \(\frac{4}{\sqrt{21}}, \frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}\)
(C) Its Cartesian form is	(III) \((-1,0,2)\)
(D) Its direction cosines are	(IV) \(\frac{x+1}{4}=\frac{y}{-1}=\frac{z-2}{2}\)

Choose the correct answer from the options given below :

The correct order of increasing reactivity of C-X bond towards nucleophilic substitution reaction (SN1) in the following compounds is
(A) Chlorobenzene
(B) Benzyl Chloride
(C) Tertiary Butyl Chloride
(D) 1-Chlorobutane
Choose the correct answer from the options given below :